I do think this is a very common American thing to value work/career so highly, as well as a generational thing. I think to an extent it's part of a particularly American ethos. I.e. when you meet someone new, one of the first questions that comes up is "what do you do?", and everyone everywhere in this country knows that the unspoken continuation is "for work?"
I think in some ways it's very similar to the common situation when a spouse dies. In that generation (and before), men did little to nothing to provide for themselves around the house. So if the husband dies first, the wife goes on for a decade+ because she's found ways to keep herself busy for the last 50 years, and she'll find something to keep herself busy afterwards. If the wife dies first, the man deteriorates quickly because suddenly he doesn't know what to do with himself (or how to do it). Often unless family steps in to help the transition, it goes that way.
I watched one of my golf buddies go through this (the retirement, not the spousal death thing) recently. We started playing golf together when I got back into the game because he was a coworker that I knew was into golf. About 2ish years ago during the downturn my company offered a voluntary separation thing, and he ended up taking it. For about 6 months he kept talking about looking for another job, and eventually that just ceased. He's got adult children (one of which still works at our company and we play golf with) who now have young grandchildren. His wife had been helping them out, but now that he's retired she's doing a bunch of church stuff and he watches the grandkids 4 days a week. He loves it! Can't imagine going back to work at this point. Feels like he's finally got the opportunity to do the things he missed out on.
For your Dad, just speculating is that he's simply afraid. He's known the work for decades. Going into retirement is a great unknown. Sounds from your description like he's got plenty that would keep him busy, and he'd probably thrive, but HE doesn't know that. And again a generational thing, the one thing that a man of that age will NEVER admit to you is fear/anxiety. I think maybe you Millennials are in the goldilocks range of emotional maturity (the Gen Zers are the other end of the spectrum), but even as a late Gen Xer, I'm ingrained with the "don't admit fear/weakness/etc emotionally, to anyone, EVER" thing... It's probably unhealthy and destructive, but... It's all I know lol...
For your uncle? I don't know... I think sometimes it's a little different with doctors. My wife's now-retired gyno was someone that had been doing it for a long time (he delivered her, actually). He was old, well past traditional retirement age, but didn't want to retire when he did. He was an "old school" doctor who largely got pushed out by the modern medical machine, but I think for him he just really enjoyed helping people. He was in good health, and now I think he's gone on to travel, etc. But for your uncle who maybe has some health problems that might stop him from having a thriving life in retirement, AND taking away perhaps his only reason for meaning? It's possible IMHO that retirement would hasten his decline, rather than slowing it.
Anyway, just spitballing here...